Reactive Power Planning Based on Fuzzy Clustering, Gray Code, and Simulated Annealing

Voltage stability constrained reactive power planning (RPP) or VAr planning is a very challenging issue in power systems. This paper proposes a new approach for modeling and solving VAr planning problem taking into account the static voltage stability constraint. First, the fuzzy clustering method is employed to select new candidate VAr source locations. Then, modified Gray code is proposed and used to represent a series of non-uniform VAr capacity intervals at different candidate buses. Under the new ordering of the VAr capacity intervals, a simplified piecewise linear function between the total transfer capability (TTC) and new VAr capacity is derived and applied as static voltage stability constraint in RPP. Finally, the RPP optimization model is solved by an enhanced simulated annealing (SA) algorithm taking advantage of the modified Gray code. In the SA algorithm, a modified definition of the neighborhood selection and a novel approach to generate new random solutions are proposed. In the case study, fuzzy clustering method, the modified Gray code, and the improved SA are applied to the IEEE 30-bus system. Test results conclude that the proposed method is a simplified and effective approach for voltage stability constrained VAr planning with contingency considered.